Self-Correcting Gottesman-Kitaev-Preskill Qubit and Gates in a Driven-Dissipative Circuit

We show that a self-correcting Gottesman-Kitaev-Preskill (GKP) qubit can be realized with a high-impedance 𝐿⁢𝐶 circuit coupled to a resistor and a Josephson junction via a controllable switch. When activating the switch in a particular stepwise pattern, the resonator relaxes into a subspace of GKP states that encode a protected qubit. Under continued operation, the resistor dissipatively error corrects the qubit against bit flips and decoherence by absorbing noise-induced entropy. We show that this leads to an exponential enhancement of the coherence time (𝑇₁ and 𝑇₂), ), even in the presence of extrinsic noise, imperfect control, and device-parameter variations. We show that the qubit supports exponentially robust single-qubit Clifford gates, implemented via appropriate control of the switch, and readout and/or initialization via supercurrent measurement. The self-correcting properties of the qubit allow it to operate at approximately 1-K temperatures and resonator 𝑄 factors down to approximately 1000 for realistic parameters, and make it amenable to parallel control through global control signals. We discuss how the effects of quasiparticle poisoning—potentially, though not necessarily, a limiting factor—might be mitigated. We finally demonstrate that a related device supports a self-correcting magic 𝑇 gate.